In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
How many triangles can you make on the 3 by 3 pegboard?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
This activity investigates how you might make squares and pentominoes from Polydron.
These practical challenges are all about making a 'tray' and covering it with paper.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you put these shapes in order of size? Start with the smallest.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
What do these two triangles have in common? How are they related?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
An activity making various patterns with 2 x 1 rectangular tiles.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
What shapes can you make by folding an A4 piece of paper?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
How many models can you find which obey these rules?
Explore the triangles that can be made with seven sticks of the
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
For this activity which explores capacity, you will need to collect some bottles and jars.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
You'll need a collection of cups for this activity.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make five differently sized squares from the tangram
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
This practical activity involves measuring length/distance.
Here is a version of the game 'Happy Families' for you to make and